Q. 103 - Precalculus Enhanced with Graphing Utilities

Question

Explain why the horizontal-line test can be used to identify one-to-one functions from a graph.

Step-by-Step Solution

Answer

Horizontal-line test states that if every horizontal line intersects the graph of a function f  in at most one point, then f  is one-to-one. That's why the horizontal test can be used to identify one-to-one functions from a graph.

Step 1. Given Information

We have to explain why the horizontal-line test can be used to identify one-to-one functions from a graph. 

Step 2. Explanation

Horizontal-line test states that if every horizontal line intersects the graph of a function f  in at most one point, then f  is one-to-one.

Let's take an example by letting the function $f\left(x\right)=x^3$, as we can depict from the following graph that the graph of the function passes the horizontal line by at most one point. Hence it is a one-to-one function.